Physics 218 Review Chapters 1- 11 and 13- 15
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Learning Goals - Chapter 1
To learn three fundamental quantities of physics and the units to measure them To keep track of significant figures in calculations To understand vectors and scalars and how to add vectors graphically To determine vector components and how to use them in calculations To understand unit vectors and how to use them with components to describe vectors To learn two ways of multiplying vectors
Chapter 1, summary
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Chapter 1 Find the net displacement of the postal truck for this journey.
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Using components, find A+B and A-B.
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Learning Goals - Chapter 2
How to describe straight line motion in terms of
Average velocity/Instantaneous velocity Average acceleration/Instantaneous acceleration
How to interpret graphs of position vs time; velocity vs time and acceleration vs time for straight line motion. How to solve problems for straight line motion with constant acceleration. How to analyze motion in a straigth line when the acceleration is NOT constant.
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Chapter 2, summary
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Chapter 2 A physics professor leaves her house and walks along the sidewalk to campus. After 5 minutes it starts to rain and she returns home. At which points is her velocity (a) zero? (b) Constant and positive? (c) Constant and negative? (d) Increasing in magnitude? (e) Decreasing in magnitude?
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A passenger train traveling at 25.0 m/s Sights a freight train 200 m ahead on the Same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. If the engineer of the passenger train applies the brakes creating an acceleration of 0.100 m/s2 in the direction opposite the train’s velocity at this point. Will there be a collision and if so where will it take place?
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Learning Goals - Chapter 3
How to represent the position of a body in 2 and 3 dimensions using vectors. How to determine the vector velocity of a body from a knowledge of its path. How to find the vector acceleration of a body and why a body can have acceleration even if its speed is constant! How to interpret the components of a body’s acceleration parallel and perpendicular to its path. How to describe the curved path followed by a projectile. The key ideas behind motion in a circular path with either constant or varying speed. How to relate the velocity of a moving body as seen from two different frames of reference. 12/10/2014
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Chapter 3, summary
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Chapter 3
An object is launched from a cliff at an angle of 50o. Use the information given in the figure to find the following: a) The initial speed of the object. b) The height of the cliff.
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An airplane pilot sets a compass course due west and maintains an airspeed of 219km/h . After flying for a time of 0.510h , she finds herself over a town a distance 121km west and a distance 22km south of her starting point. a)Find the magnitude of the wind velocity. b)Find the direction of the wind velocity. Express your answer as an angle measured south of west. c)If the wind velocity is 36km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 219km/h.
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1)
An air-traffic controller observes two planes on the radar directly east of the airport. One is at a radial distance d1 and angle θ1 above the horizontal, the other is at a distance d2 and angle θ2. What is the distance between the two planes? (Given d1, d2, θ1, and θ2 find the distance d12 between the planes.)
T. Stiegler
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A basketball player releases the ball from a height h1 at an angle θ and initial velocity v0 in an attempt to put the ball into the basket which is at height h2 and a horizontal distance d. Calculate the distance d if the ball is to make it into the basket. (given h1, h2, θ, and v0 find d)
T. Stiegler
h1
d
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A coyote wearing an ACME rocket pack is traveling along a road at a constant velocity v0 and spots a road runner directly ahead at a distance d0. The road runner is standing still but spots the coyote at t = 0 and races with constant acceleration a toward a cave opening which is at a distance dc from the road runner. Find the velocity v0 such that the coyote just manages to catch the road runner at the entrance to the cave. (given d0, dc, and a find v0 so that the poor hungry coyote gets to have roast road runner for dinner.) d0 v0
T. Stiegler
dc
a
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A carnival ride is a large cylinder that rotates along its axis with a frequency f revolutions per second. People are supposed to stand along the wall of the cylinder at radius R and feel an acceleration 5g when the cylinder is rotating. Find the radius R such that this is the case.
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A ball is dropped (from rest) from a window at height h and is seen to reach the ground in a certain time. The ball-dropper then climbs to a height 2h but wants the ball to reach the ground in the original time. Find the velocity v0 that must be given to this ball to achieve the goal.
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A cannon ball is fired with a velocity v0 at an angle α from a height y0 = 0 from position x0 = 0. It strikes a cliff a distance D away at a height H. What is the value of the height H in terms of the other given variables.
H
V0 , α D T. Stiegler
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Learning Goals - Chapter 4
What the concept of force means in physics and why forces are vectors. The significance of the net force on an object and what happens when the net force is zero. The relationship among the net force on an object, the object’s mass and its acceleration. How forces that two bodies exert on each other are related.
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Chapter 4 How large a force, F, is needed for the component parallel to the ramp to be 60.0 N? How large will the component perpendicular to the ramp be under these conditions?
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Two boxes are connected by a light rope as shown. A constant upward force F = 80 N is applied to the system. Starting from rest, box B descends 12.0 m in 4.00 seconds. The tension in the rope between the two boxes is 36.0 N. A) what is the mass of the box B. B) What is the mass of box A?
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7)
Consider the block shown at the right. The block is on an incline with angle θ and a person is pulling on a rope with force F at an angle α relative to the surface of the ramp as shown. The mass of the block is m and there is no friction. What is the total force acting on the block along the line parallel to F the ramp (along the dotted line)?
α
θ T. Stiegler
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F A block of mass M1 is attached to a mass M2 with a massless rope as shown. A force F is causing the two blocks to accelerate upward. What is the tension in the rope in terms of M1, M2, F, and g?
M1
T=? M2
T. Stiegler
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Learning Goals – Chapter 5
How to use Newton’s Laws to solve problems involving forces that act on a body in equilibrium. How to use Newton’s 2nd Law to solve problems involving the forces that act on an accelerating body. The nature of the different types of frictional forces: Static, Kinetic, Rolling, and Fluid Resistance, and how to solve problems that involve these forces. How to solve problems involving forces that act on a body moving along a circular path.
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5.99) Block A, with a weight 3w slides down an incline of 36.9 degrees at a constant speed. Plank B, weight w, rests on top of block A. A) draw a free body diagram of block A. B) If coefficient of kinetic friction is the same between a-b and a-ramp, solve for its value.
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5.119) A small bead can slide without friction on a circular hoop of radius 0.100 m. The hoop rotates at a constant rate of 4.00 rev/sec about the vertical. Find the angle beta that the bead will make when in equilibrium.
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Learning Goals – Chapter 6
What it means for a force to do work and how to calculate the amount of work done. The definition of kinetic energy of a body and what it means physically. How the total work done on a body changes the body’s kinetic energy and how to use this principle to solve problems in mechanics. How to use the relationship between the total work and the change in kinetic energy when the forces are not constant, the body follows a curved path or both. How to solve problems involving power.
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6.75) A small block of mass .090 kg is attached to a cord passing through a hole in a frictionless horizontal surface as shown. The block is originally revolving at a distance of 0.40m with a speed of 0.70 m/s. The cord is then pulled from below, changing the radius of the circle to 0.10 m. At this new distance the speed of the block is observed to be 2.80 m/s. A) What was the tension in the cord in the original configuration? B) find the work done by the person pulling on the cord. 12/10/2014
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6.77) A block of ice of mass 4.00 kg is initially at rest on a frictionle ss surface. A worker then applies a force F to it resulting in motion along the x - axis with x(t) given by thefollowing : x(t ) t 2 t 3 , where 0.20 m/s 2 and 0.020 m/s 3 a) Find the velocity of the block of ice at t 4.00 s. b) Calculate the work done by theforce F duringthe first 4.00 s of motion.
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Learning Goals- chapter 7
How to use the concept of gravitational potential energy in problems that involve vertical motion. How to use the concept of elastic potential energy in problems involving a moving body attached to a stretched or compressed spring. The distinction between conservative and non-conservative forces and how to solve problems involving both kinds of forces. How to calculate the properties of a conservative force if you know the corresponding potential energy function. How to use energy diagrams to understand the motion of an object moving in a straight line under the influence of a conservative force.
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7.42) A 2.00 kg block is pushed against a spring with a force constant of k=400 N/m and negligible mass, compressing it 0.220m. A) What is the speed of the block on the horizontal. B) How high up the ramp will the block slide before coming to rest?
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7.46) A car in an amusement park rolls without friction along the track as shown. If it starts from rest at point A at height h above the horizontal, what is the minimum height that it must be released with to make it through the loop without falling off at B? 12/10/2014
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Learning Goals - Chapter 8
The meaning of the momentum of a particle(system) and how the impulse of the net force acting on a particle causes the momentum to change. The conditions under which the total momentum of the system of particles is constant (conserved). How to solve two-body collision problems. The distinction between elastic, inelastic and completely inelastic collisions. The definition of the center of mass of a system and what determines how the center of mass moves.
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Definition of Momentum (revisited) dv d FNet m dt dt (mv ) we defined the quantity mv p mv as the momentum of the particle dp FNet dt as an alternate form of Newton's 2nd Law 12/10/2014
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The Definition of Impulse J Fnet (t 2 t1 ) Ft assuming a constant net force
p2 p1 Fnet t t 2 1
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Conservation of Momentum
If the vector sum of the external forces on a system is zero, the total momentum of the system is conserved.
dp FNet 0 dt and the momentum of the systemis constant 12/10/2014
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Figure 8.13
Figure 8.24
Center of Mass of a system m1r1 m2 r2 m3r3 mi ri rcenter of mass m1 m2 m3 mi
Where is this point located in a system of discrete masses? In a continuous mass distribution?
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Taking the derivative with respect to time gives interesting results dri m d m1r1 m2 r2 m3r3 i dt vcenter of mass ( ) dt m1 m2 m3 mi ( mi )vcenter of mass mi vi ptotal
m v ii
m
i
d v mi i m a d m1v1 m2 v2 m3v3 dt i i acenter of mass ( ) dt m1 m2 m3 mi mi ( mi ) acenter of mass mi ai Finternal FExternal FNet External 12/10/2014
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Learning Goals - Chapter 9
How to describe the rotation of a rigid body in terms of angular coordinate, angular velocity and angular acceleration. How to analyze rigid body rotation when angular acceleration is constant. How to relate the rotation of a rigis body to the linear velocity and linear acceleration of a point on the body. The meaning of a body’s moment of inertia about an axis of rotation and how it relates to the rotational kinetic energy. How to calculate the moment of inertia of various bodies. How to describe the motion of an object in “polar coordinates”
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Table 9.1
Moment of Inertia M oment of Inertia : rotational analog of mass I m1r12 m1r12 m1r12 mi ri 2
The Parallel Axis Theorem I P I cm Md
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Table 9.2
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The mass is released from rest, 2m above the floor: find the speed of the system just before the weight hits the floor.
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Learning Goals - Chapter 10
What is meant by the torque produced by a force. How the net torque on a body affects the rotational motion of the body. How to analyze the motion of a body that both rotates and moves as a whole through space. How to solve problems that involve work and power for rotating bodies. What is meant by the angular momentum of a particle or rigid body. How the angular momentum of a system changes with time. Why a spinning gyroscope goes through the curious motion called precession.
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r F r F sin ,
where the direction is given by the" right hand rule"
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(rotational analog of Newton's 2nd Law)
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z
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Rotation and Translation at the same time the total Kinetic Energy of such a system 2 ' 2 1 1 K 2 mi vi 2 mi (vcm vi ) giving the total Kinetic Energy of such a system K Mv I cm 1 2
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Combined Rotation and Translation Dynamics
Fext Macm
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I cm z
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The mass is released from rest, 2m above the floor: a) find the angular acceleration of the spinning system as the weight falls and b) the tension in the string.
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Work Done for rotational motion 2 Wby a torque F dl Ftan Rd z d 1
d z d z d ( I z )d I d I d z I z d z dt dt 2
W I z d z 12 I22 12 I12 1
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Angular Momentum L r p r mv for a point mass, and dL r F dt
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Conservation of Angular Momentum when the external torques present 0 dL dt 0 or, L constant
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Learning Goals - Chapter 11
The conditions that must be satisified for a body or structure to be in “equilibrium”. What is meant by the “center of gravity” and how it is related to the bodies stability. How to solve problems that involve rigid bodies in equilibrium.
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Equilibrium Conditions A body in equilibriu m M UST satisfy these two conditions F 0 0 about ANY point wechoose 12/10/2014
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Learning Goals - Chapter 13
How to calculate the gravitational forces that two bodies exert on each other. How to relate the weight of an object to the general expression for gravitational force. How to use and interpret the generalized expression for gravitational potential energy. How to relate the speed, orbital period, and mechanical energy of a satellite in circular orbit. The laws that describe the motions of the planets and how to work with these laws (Kepler’s Laws)
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The Universal Law of Gravity Gm1m2 Fg , 2 r12 with the force acting along the line joining the centers of the two masses
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Gravitational Potential Energy Wg Fg dl (U 2 U1 ) r2
r1 r2
GmE m GmE m GmE m dr ( ) 2 r r2 r1 r1 GmE m U constant r 12/10/2014
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Kepler’s Laws
Each Planet moves in an elliptical orbit with the sun at one focus of the ellipse. A line from the sun to a given planet sweeps out equal areas in equal times. The periods of the planets are proportional to the 3/2 power of the major axis lengths of their orbits.
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Figure 13.18
The First Law
Figure 13.19
Kepler’s Second Law
dA 1 2 d 2r dt dt L 1 1 2 rv 2 r v 2m
Kepler’s Third Law Following from our earlier calculatio n for a circular orbit, for ellipitica l orbits we replace the radius, r, with the semi - major axis length, a. 2a 2 T GmS 3
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Learning Goals - Chapter 14 • • • • •
• • •
To describe oscillations in terms of amplitude, period, frequency and angular frequency To do calculations with simple harmonic motion To analyze simple harmonic motion using energy To apply the ideas of simple harmonic motion to different physical situations To analyze the motion of a simple pendulum To examine the characteristics of a physical pendulum To explore how oscillations die out To learn how a driving force can cause resonance
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Learning Goals - Chapter 15
To study the properties and varieties of mechanical waves To relate the speed, frequency, and wavelength of periodic waves To interpret periodic waves mathematically To calculate the speed of a wave on a string To calculate the energy of mechanical waves To understand the interference of mechanical waves To analyze standing waves on a string To investigate the sound produced by stringed instruments
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